Return method : application to controllability

J.-M. Coron

Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993)

  • page 1-11

How to cite


Coron, J.-M.. "Return method : application to controllability." Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993): 1-11. <>.

author = {Coron, J.-M.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {return method; local controllability; periodic trajectory; periodic feedback; incompressible 2-D Euler equation; Laplace equation},
language = {eng},
pages = {1-11},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Return method : application to controllability},
url = {},
year = {1992-1993},

AU - Coron, J.-M.
TI - Return method : application to controllability
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1992-1993
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 11
LA - eng
KW - return method; local controllability; periodic trajectory; periodic feedback; incompressible 2-D Euler equation; Laplace equation
UR -
ER -


  1. [A-G] A.A. Agrachev and R.V. Gamkerelidze, Local controllability and semigroup diffeomorphisms, Steklov Math. Institute, Preprint (1993). MR1232941
  2. [B-S] B.S.R.M. Bianchini and G. Stefani, Controllability along a trajectory: a variational approach, Preprint (1992). Zbl0797.49015
  3. [Ch] W.L. Chow, Uber systeme von linearen partiellen differentialgleichungen ester ordnung, Math. Ann.11 (1940-41), 98-105. JFM65.0398.01
  4. [Co1] J.-M. Coron, Global asymptotic stabilization for controllable systems without drift, Math. Control Signals and Systems, 5 (1992), 227-232. Zbl0699.93075MR1164379
  5. [Co2] J.-M. Coron, Stabilization, of controllable systems, Preprint, CMLA, April 1993. 
  6. [Co3] J.-M. Coron, Links between local controllability and local continuous stabilization, Preprint ETH-Zürich and Université Paris-Sud, October 1991, and NOLCO'S 92, M. Fliess ed., Bordeaux, June 1992, 477-482. 
  7. [Co4] J.-M. Coron, Linearized control systems and applications to smooth stabilization, Preprint Université Paris-Sud, February 1992, to appear in SIAM J. on Control and Optimization. Zbl0796.93097MR1261144
  8. [Co5] J.-M. Coron, Contrôlabilité exacte frontière de l'équation des fluides parfaits incompressibles bidimensionnels, Preprint, CMLA, May 1993. Zbl0781.76013MR1233425
  9. [C-P] J.-M. Coron, J.-B. Pomet, A remark on the design of time-varying stabilizing feedback laws for controllable systems without drift, NOLCO'S 92, M. Fliess ed., Bordeaux, June 1992, 413-417. 
  10. [Ha] R.S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Am. Math. Soc., 7 (1982), 65-222. Zbl0499.58003MR656198
  11. [He] H. Hermes, Control systems wich generate decomposable Lie algebras, J. Differential Equations, 44 (1982), 166-187. Zbl0496.49021MR657777
  12. [K] M. Kawski, High-order small-time local controllability, in Controllability and Optimal Control, H.J. Sussmann ed., Monographs and Textbooks in Pure and Applied Mathematics113, M. Dekker, Inc.New York (1990), 431-467. Zbl0703.93013MR1061394
  13. [L1] J.-L. Lions, Exact controllability, stabilization and perturbation for distributed systems, SIAM Rev.30 (1988), 1-68. Zbl0644.49028MR931277
  14. [L2] J.-L. Lions, Contrôlabilité exacte, Masson, Paris, (1988). MR953547
  15. [L3] J.-L. Lions, Are there connections between turbulence and controllability ? 9th INRIA International Conference, Antibes, June 12-15, 1990. 
  16. [L4] J.-L. Lions, Exact controllability for distributed systems. Some trends and some problems, in Applied and Industrial Mathematics, R. Spigler ed. Kluwer Academic Publishers, Dordrecht, Boston, London, (1991), 59-84. Zbl0735.93006MR1147191
  17. [P] J.-B. Pomet, Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift, Systems and Control Letters, 18 (1992), 93-98. Zbl0744.93084MR1149359
  18. [R] D.L. Russell, Exact boundary value controllability theorems for wave and heat processes in star- complemented regions, in Differential Games and Control Theory, Roxin, Liu and Sternberg eds., Marcel Dekker, New York, (1974). Zbl0308.93007MR467472
  19. [S-M] L.M. Silverman, H.E. Meadows, Controllability and observability in time variable linear systems, SIAM J. on Control and Optimization, 5 (1967), 64-73. Zbl0163.11001MR209043
  20. [So1] E.D. Sontag, Finite dimensional open-loop control generator for nonlinear systems, Int. J. Control, 47 (1988), 537-556. Zbl0641.93035MR929174
  21. [So2] E.D. Sontag, Mathematical Control Theory Deterministic Finite Dimensional Systems, Texts in Applied Mathematics6, Springer-Verlag, New York-Berlin-Heidelberg-London-Paris-Tokyo- Hong Kong, (1990). Zbl0703.93001MR1070569
  22. [So3] E.D. Sontag, Universal nonsingular controls, Systems and Control Letters, 19 (1992), 221-224. Zbl0763.93038MR1180510
  23. [Su1] H.J. Sussmann, Lie brackets and local controllability: a sufficient condition for scalar input systems, SIAM J. on Control and Optimization, 21 (1983), 686-713. Zbl0523.49026MR710995
  24. [Su2] H.J. Sussmann, A general theorem on local controllability, SIAM J. on Control and Optimization, 25 (1987), 158-194. Zbl0629.93012MR872457
  25. [S-J] H.J. Sussmann, V. Jurdjevic, Controllability on nonlinear systems, J. Diff. Equations, 12 (1972), 95-116. Zbl0242.49040MR338882

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